Answer:
- ∠D = 45°
- ∠E = 95°
- ∠F = 85°
- ∠G = 135°
Explanation:
You want the measures of each angle in the quadrilateral marked D = (2x+18)°, E = (8x -13)°, F = (6x+4)°, G = 10x°.
Sum of angles
The sum of angles in a quadrilateral is 360°, so we have ...
D +E +F +G = 360°
(2x+18)° +(8x-13)° +(6x+4)° +10x° = 360°
26x +9 = 360 . . . . . . . . . divide by °, collect terms
26x = 351 . . . . . . . . . subtract 9
x = 13.5 . . . . . . . . divide by 26
Angle measures
The angle measures are found by using this value of x in the expression for each:
D = (2(13.5) +18)° = 45°
E = (8(13.5) -13)° = 95°
F = (6(13.5) +4)° = 85°
G = 10(13.5)° = 135°
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Additional comment
We note that left-side angles total 180°, as do right-side angles. This means DE║FG and the figure is a trapezoid.
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